I believe I am the kind of person who would just say "Go ahead, shut it down if that's the only alternative. If you would like me to sign a deal to restructure the company, then I'll happily do it, but the company needs to pay me a one time cash bonus that reflects the value of the shares that I am forfeiting".
I am not naive enough to believe it would work, as they would probably find a way to screw me regardless, but my stance would be firm.
After my experience with startups I have become completely intolerant to corporate greed and injustice, so these days I am purely in a business transaction with my employer and I know exactly what to expect and when to expect it (which is why I get paid in RSUs rather than stock options). I like to think I wouldn't fall prey to this sort of petty begging.